TSTP Solution File: KRS139+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : KRS139+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 23:19:20 EDT 2024

% Result   : Theorem 3.21s 1.77s
% Output   : Refutation 3.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   64 (  13 unt;  11 typ;   0 def)
%            Number of atoms       :  176 (   5 equ;   0 cnn)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  373 (  89   ~;  73   |;  27   &; 171   @)
%                                         (   3 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   6   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :   35 (   0   ^  33   !;   2   ?;  35   :)

% Comments : 
%------------------------------------------------------------------------------
thf(cowlThing_type,type,
    cowlThing: $i > $o ).

thf(cowlNothing_type,type,
    cowlNothing: $i > $o ).

thf(xsd_string_type,type,
    xsd_string: $i > $o ).

thf(xsd_integer_type,type,
    xsd_integer: $i > $o ).

thf(iAntwerp_type,type,
    iAntwerp: $i ).

thf(rpath_type,type,
    rpath: $i > $i > $o ).

thf(iGhent_type,type,
    iGhent: $i ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk2_type,type,
    sk2: $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(4,axiom,
    ! [A: $i] :
      ( ( xsd_string @ A )
    <=> ~ ( xsd_integer @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).

thf(20,plain,
    ! [A: $i] :
      ( ( ( xsd_string @ A )
       => ~ ( xsd_integer @ A ) )
      & ( ~ ( xsd_integer @ A )
       => ( xsd_string @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(21,plain,
    ( ! [A: $i] :
        ( ( xsd_string @ A )
       => ~ ( xsd_integer @ A ) )
    & ! [A: $i] :
        ( ~ ( xsd_integer @ A )
       => ( xsd_string @ A ) ) ),
    inference(miniscope,[status(thm)],[20]) ).

thf(22,plain,
    ! [A: $i] :
      ( ( xsd_integer @ A )
      | ( xsd_string @ A ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(24,plain,
    ! [A: $i] :
      ( ( xsd_integer @ A )
      | ( xsd_string @ A ) ),
    inference(simp,[status(thm)],[22]) ).

thf(1,conjecture,
    ( ! [A: $i] :
        ( ( cowlThing @ A )
        & ~ ( cowlNothing @ A ) )
    & ! [A: $i] :
        ( ( xsd_string @ A )
      <=> ~ ( xsd_integer @ A ) )
    & ( cowlThing @ iAntwerp )
    & ( rpath @ iAntwerp @ iGhent )
    & ( cowlThing @ iGhent ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).

thf(2,negated_conjecture,
    ~ ( ! [A: $i] :
          ( ( cowlThing @ A )
          & ~ ( cowlNothing @ A ) )
      & ! [A: $i] :
          ( ( xsd_string @ A )
        <=> ~ ( xsd_integer @ A ) )
      & ( cowlThing @ iAntwerp )
      & ( rpath @ iAntwerp @ iGhent )
      & ( cowlThing @ iGhent ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(9,plain,
    ~ ( ! [A: $i] :
          ( ( cowlThing @ A )
          & ~ ( cowlNothing @ A ) )
      & ! [A: $i] :
          ( ( ( xsd_string @ A )
           => ~ ( xsd_integer @ A ) )
          & ( ~ ( xsd_integer @ A )
           => ( xsd_string @ A ) ) )
      & ( cowlThing @ iAntwerp )
      & ( rpath @ iAntwerp @ iGhent )
      & ( cowlThing @ iGhent ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10,plain,
    ~ ( ! [A: $i] : ( cowlThing @ A )
      & ~ ? [A: $i] : ( cowlNothing @ A )
      & ! [A: $i] :
          ( ( xsd_string @ A )
         => ~ ( xsd_integer @ A ) )
      & ! [A: $i] :
          ( ~ ( xsd_integer @ A )
         => ( xsd_string @ A ) )
      & ( cowlThing @ iAntwerp )
      & ( rpath @ iAntwerp @ iGhent )
      & ( cowlThing @ iGhent ) ),
    inference(miniscope,[status(thm)],[9]) ).

thf(13,plain,
    ( ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_integer @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ ( cowlThing @ iAntwerp )
    | ~ ( rpath @ iAntwerp @ iGhent )
    | ~ ( cowlThing @ iGhent ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(8,axiom,
    rpath @ iGhent @ iAntwerp,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).

thf(29,plain,
    rpath @ iGhent @ iAntwerp,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( rpath @ A @ B )
     => ( rpath @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).

thf(25,plain,
    ! [A: $i,B: $i] :
      ( ( rpath @ A @ B )
     => ( rpath @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(26,plain,
    ! [B: $i,A: $i] :
      ( ~ ( rpath @ A @ B )
      | ( rpath @ B @ A ) ),
    inference(cnf,[status(esa)],[25]) ).

thf(48,plain,
    ! [B: $i,A: $i] :
      ( ( rpath @ B @ A )
      | ( ( rpath @ iGhent @ iAntwerp )
       != ( rpath @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[29,26]) ).

thf(49,plain,
    rpath @ iAntwerp @ iGhent,
    inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( iGhent )),bind(B,$thf( iAntwerp ))]]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).

thf(15,plain,
    ! [A: $i] :
      ( ( cowlThing @ A )
      & ~ ( cowlNothing @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(16,plain,
    ( ! [A: $i] : ( cowlThing @ A )
    & ~ ? [A: $i] : ( cowlNothing @ A ) ),
    inference(miniscope,[status(thm)],[15]) ).

thf(18,plain,
    ! [A: $i] : ( cowlThing @ A ),
    inference(cnf,[status(esa)],[16]) ).

thf(17,plain,
    ! [A: $i] :
      ~ ( cowlNothing @ A ),
    inference(cnf,[status(esa)],[16]) ).

thf(19,plain,
    ! [A: $i] :
      ~ ( cowlNothing @ A ),
    inference(simp,[status(thm)],[17]) ).

thf(62,plain,
    ( ~ $true
    | $false
    | ( xsd_integer @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ $true
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[13,49,18,19]) ).

thf(63,plain,
    ( ( xsd_integer @ sk3 )
    | ~ ( xsd_integer @ sk4 ) ),
    inference(simp,[status(thm)],[62]) ).

thf(11,plain,
    ( ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_string @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ ( cowlThing @ iAntwerp )
    | ~ ( rpath @ iAntwerp @ iGhent )
    | ~ ( cowlThing @ iGhent ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(34,plain,
    ( ~ $true
    | $false
    | ( xsd_string @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ $true
    | ~ ( rpath @ iAntwerp @ iGhent )
    | ~ $true ),
    inference(rewrite,[status(thm)],[11,18,19]) ).

thf(35,plain,
    ( ( xsd_string @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ ( rpath @ iAntwerp @ iGhent ) ),
    inference(simp,[status(thm)],[34]) ).

thf(56,plain,
    ( ( xsd_string @ sk3 )
    | ~ ( xsd_integer @ sk4 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[35,49]) ).

thf(57,plain,
    ( ( xsd_string @ sk3 )
    | ~ ( xsd_integer @ sk4 ) ),
    inference(simp,[status(thm)],[56]) ).

thf(60,plain,
    ! [A: $i] :
      ( ( xsd_string @ A )
      | ( xsd_string @ sk3 )
      | ( ( xsd_integer @ A )
       != ( xsd_integer @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[24,57]) ).

thf(61,plain,
    ( ( xsd_string @ sk4 )
    | ( xsd_string @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( sk4 ))]]) ).

thf(12,plain,
    ( ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_string @ sk3 )
    | ~ ( xsd_string @ sk4 )
    | ~ ( cowlThing @ iAntwerp )
    | ~ ( rpath @ iAntwerp @ iGhent )
    | ~ ( cowlThing @ iGhent ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(43,plain,
    ( ~ $true
    | $false
    | ( xsd_string @ sk3 )
    | ~ ( xsd_string @ sk4 )
    | ~ $true
    | ~ ( rpath @ iAntwerp @ iGhent )
    | ~ $true ),
    inference(rewrite,[status(thm)],[12,18,19]) ).

thf(44,plain,
    ( ( xsd_string @ sk3 )
    | ~ ( xsd_string @ sk4 )
    | ~ ( rpath @ iAntwerp @ iGhent ) ),
    inference(simp,[status(thm)],[43]) ).

thf(54,plain,
    ( ( xsd_string @ sk3 )
    | ~ ( xsd_string @ sk4 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[44,49]) ).

thf(55,plain,
    ( ( xsd_string @ sk3 )
    | ~ ( xsd_string @ sk4 ) ),
    inference(simp,[status(thm)],[54]) ).

thf(76,plain,
    ( ( xsd_string @ sk3 )
    | ( ( xsd_string @ sk4 )
     != ( xsd_string @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[61,55]) ).

thf(77,plain,
    xsd_string @ sk3,
    inference(pattern_uni,[status(thm)],[76:[]]) ).

thf(23,plain,
    ! [A: $i] :
      ( ~ ( xsd_string @ A )
      | ~ ( xsd_integer @ A ) ),
    inference(cnf,[status(esa)],[21]) ).

thf(84,plain,
    ! [A: $i] :
      ( ~ ( xsd_integer @ A )
      | ( ( xsd_string @ sk3 )
       != ( xsd_string @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[77,23]) ).

thf(85,plain,
    ~ ( xsd_integer @ sk3 ),
    inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( sk3 ))]]) ).

thf(89,plain,
    ( $false
    | ~ ( xsd_integer @ sk4 ) ),
    inference(rewrite,[status(thm)],[63,85]) ).

thf(90,plain,
    ~ ( xsd_integer @ sk4 ),
    inference(simp,[status(thm)],[89]) ).

thf(97,plain,
    ! [A: $i] :
      ( ( xsd_string @ A )
      | ( ( xsd_integer @ A )
       != ( xsd_integer @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[24,90]) ).

thf(98,plain,
    xsd_string @ sk4,
    inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( sk4 ))]]) ).

thf(14,plain,
    ( ~ ( cowlThing @ sk1 )
    | ( cowlNothing @ sk2 )
    | ( xsd_integer @ sk3 )
    | ~ ( xsd_string @ sk4 )
    | ~ ( cowlThing @ iAntwerp )
    | ~ ( rpath @ iAntwerp @ iGhent )
    | ~ ( cowlThing @ iGhent ) ),
    inference(cnf,[status(esa)],[10]) ).

thf(66,plain,
    ( ~ $true
    | $false
    | ( xsd_integer @ sk3 )
    | ~ ( xsd_string @ sk4 )
    | ~ $true
    | ~ $true
    | ~ $true ),
    inference(rewrite,[status(thm)],[14,49,18,19]) ).

thf(67,plain,
    ( ( xsd_integer @ sk3 )
    | ~ ( xsd_string @ sk4 ) ),
    inference(simp,[status(thm)],[66]) ).

thf(87,plain,
    ( $false
    | ~ ( xsd_string @ sk4 ) ),
    inference(rewrite,[status(thm)],[67,85]) ).

thf(88,plain,
    ~ ( xsd_string @ sk4 ),
    inference(simp,[status(thm)],[87]) ).

thf(99,plain,
    $false,
    inference(rewrite,[status(thm)],[98,88]) ).

thf(100,plain,
    $false,
    inference(simp,[status(thm)],[99]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : KRS139+1 : TPTP v8.2.0. Released v3.1.0.
% 0.11/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n015.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sat May 18 22:18:24 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 0.99/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.15/0.96  % [INFO] 	 Parsing done (94ms). 
% 1.15/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.47/1.16  % [INFO] 	 nitpick registered as external prover. 
% 1.47/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.78/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ... 
% 1.81/1.24  % [INFO] 	 Axiom selection finished. Selected 6 axioms (removed 0 axioms). 
% 1.81/1.25  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 1.81/1.25  % [INFO] 	 Type checking passed. 
% 1.81/1.26  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 3.21/1.76  % [INFO] 	 Killing All external provers ... 
% 3.21/1.77  % Time passed: 1234ms (effective reasoning time: 796ms)
% 3.21/1.77  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.21/1.77  % Axioms used in derivation (4): axiom_1, axiom_5, axiom_2, axiom_0
% 3.21/1.77  % No. of inferences in proof: 53
% 3.21/1.77  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1234 ms resp. 796 ms w/o parsing
% 3.39/1.84  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.39/1.84  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------